Music synthesizer generate audio tones. Many synthesizers generate their tones by using one or more oscillators. It is very common to use several oscillators in a single synthesizer voice but with at least one oscillator detuned. That is to say, that oscillator is oscillating at a slightly different frequency to at least one other oscillator. As a consequence of interference, this results in a periodically changing resulting signal due to the varying phase difference between them.
When there are two slightly detuned sine waves, the resulting signal is perceived as a single sine wave with a sinusoidal amplitude modulation varying with frequency. The frequency of this amplitude modulation is called the “beat frequency”. This can be expressed as follows:
Oscillator A:a(t) = sin (2π fa t)Oscillator B:b(t) = sin (2π fb t)The resulting signal: s(t)= a(t) + b(t)= sin (2π fa t) + sin (2π fb t)= 2 sin (2π [fa + fb] t/2) cos (2π [fa − fb] t/2)
where fa is the frequency of oscillator A, fb is the frequency of oscillator B, a(t) is the output from oscillator A and b(t) is the output from oscillator B.
More often than not, there are two detuned oscillators producing more complex waveforms. Complex waveforms include waveforms in shapes which differ more or less from a perfect sine wave, e.g. a sawtooth or rectangular wave and can be decomposed into a sum of harmonic sine waves (the overtones or partial frequencies). The resulting interference from such complex waveforms is not a simple amplitude modulation but a complex timbre variation. This is because each pair of harmonic overtones has to be treated separately. However, the timbre variation when mixing two slightly detuned oscillators is still periodic with a beat frequency. Moreover, that beat frequency is equal to the difference between the two frequencies of the mixed detuned oscillators.
Synthesizer oscillators are usually tuned in a chromatic scale that consists of equal semitone intervals. An interval is defined by a certain frequency ratio between two tones. Twelve semitone interval steps result in an octave interval which is defined as a frequency ratio of 2:1. Hence, each semitone is the twelfth root of 2 or approximately 1.06. A semitone can be further divided into cents. A cent is one hundredth of a semitone. Thus, one cent is a 1200th root of 2 or approximately 1.0006.
In the prior art, synthesizer oscillators have been detuned by setting a certain detune interval which was usually measured in cents. Due to the fact that the detune interval defines the ratio between the detuned frequency and the nominal frequency, the frequency deviation itself is proportional to the nominal frequency. For example, if the nominal oscillator frequency was 1000 Hz, then applying a detune interval of 10 cent (approx. 1.006) would result in a detuned oscillator frequency of 1006 Hz and a beat frequency of 6 Hz. However, with the same detune interval of 10 cent at the next octave, the nominal frequency would be 2000 Hz with the detuned oscillator frequency of 2012 Hz and a beat frequency of 12 Hz. Accordingly, at a given detune interval the detuned oscillator has a frequency deviation which is proportional to its nominal frequency. Hence, when mixing detuned oscillators, the resulting signal has a beat frequency which varies with the pitch and doubles with each octave.
In order to accommodate for this beat frequency, a compromise is reached but often such audio tones have a beat frequency which is relatively too slow at lower tones and too high at higher tones.
An aim of the present invention is to provide a music synthesizer whereby sounds are generated with an optimum beat across a large range of tones.